%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET909+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:15:44 PM UTC 2026
% Result : Theorem 0.15s 5.45s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 24 ( 13 unt; 0 def)
% Number of atoms : 79 ( 41 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 93 ( 38 ~; 38 |; 11 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 63 ( 7 sgn 44 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t50_zfmisc_1,conjecture,
! [X1,X2,X3] : set_union2(unordered_pair(X1,X2),X3) != empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_zfmisc_1) ).
fof(d1_xboole_0,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(d2_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_union2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X2)
| in(X4,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(commutativity_k2_xboole_0,axiom,
! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(d2_tarski,axiom,
! [X1,X2,X3] :
( X3 = unordered_pair(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( X4 = X2
| X4 = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
fof(c_0_5,negated_conjecture,
~ ! [X1,X2,X3] : set_union2(unordered_pair(X1,X2),X3) != empty_set,
inference(assume_negation,[status(cth)],[t50_zfmisc_1]) ).
fof(c_0_6,negated_conjecture,
~ ! [X1,X2,X3] : set_union2(unordered_pair(X1,X2),X3) != empty_set,
inference(fof_simplification,[status(thm)],[c_0_5]) ).
fof(c_0_7,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[d1_xboole_0]) ).
fof(c_0_8,plain,
! [X24,X25,X26,X27,X28,X29,X30,X31] :
( ( X31 = set_union2(X29,X30)
| in(esk3_3(X29,X30,X31),X30)
| in(esk3_3(X29,X30,X31),X29)
| in(esk3_3(X29,X30,X31),X31) )
& ( X31 = set_union2(X29,X30)
| ~ in(esk3_3(X29,X30,X31),X31)
| ~ in(esk3_3(X29,X30,X31),X30) )
& ( X31 = set_union2(X29,X30)
| ~ in(esk3_3(X29,X30,X31),X31)
| ~ in(esk3_3(X29,X30,X31),X29) )
& ( X26 != set_union2(X24,X25)
| in(X28,X26)
| ~ in(X28,X25) )
& ( X26 != set_union2(X24,X25)
| in(X28,X26)
| ~ in(X28,X24) )
& ( X26 != set_union2(X24,X25)
| in(X27,X25)
| in(X27,X24)
| ~ in(X27,X26) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d2_xboole_0])])])])])])]) ).
fof(c_0_9,negated_conjecture,
set_union2(unordered_pair(esk6_0,esk7_0),esk8_0) = empty_set,
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
fof(c_0_10,plain,
! [X9,X10] : set_union2(X9,X10) = set_union2(X10,X9),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(c_0_11,plain,
! [X11,X12,X13] :
( ( X13 = empty_set
| in(esk1_1(X13),X13) )
& ( ~ in(X12,X11)
| X11 != empty_set ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])])])]) ).
cnf(c_0_12,plain,
( X3 != set_union2(X4,X2)
| ~ in(X1,X2)
| in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,negated_conjecture,
set_union2(unordered_pair(esk6_0,esk7_0),esk8_0) = empty_set,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,plain,
( ~ in(X2,X1)
| X1 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_16,plain,
! [X15,X16,X17,X18,X19,X20,X21,X22] :
( ( X22 = unordered_pair(X20,X21)
| esk2_3(X20,X21,X22) = X21
| esk2_3(X20,X21,X22) = X20
| in(esk2_3(X20,X21,X22),X22) )
& ( X22 = unordered_pair(X20,X21)
| ~ in(esk2_3(X20,X21,X22),X22)
| esk2_3(X20,X21,X22) != X21 )
& ( X22 = unordered_pair(X20,X21)
| ~ in(esk2_3(X20,X21,X22),X22)
| esk2_3(X20,X21,X22) != X20 )
& ( X17 != unordered_pair(X15,X16)
| in(X19,X17)
| X19 != X16 )
& ( X17 != unordered_pair(X15,X16)
| in(X19,X17)
| X19 != X15 )
& ( X17 != unordered_pair(X15,X16)
| X18 = X16
| X18 = X15
| ~ in(X18,X17) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d2_tarski])])])])])])]) ).
cnf(c_0_17,plain,
( ~ in(X1,X3)
| in(X1,set_union2(X2,X3)) ),
inference(er,[status(thm)],[c_0_12]) ).
cnf(c_0_18,negated_conjecture,
set_union2(esk8_0,unordered_pair(esk6_0,esk7_0)) = empty_set,
inference(rw,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_19,plain,
~ in(X1,empty_set),
inference(er,[status(thm)],[c_0_15]) ).
cnf(c_0_20,plain,
( X3 != unordered_pair(X2,X4)
| X1 != X2
| in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_21,negated_conjecture,
~ in(X1,unordered_pair(esk6_0,esk7_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]) ).
cnf(c_0_22,plain,
in(X1,unordered_pair(X1,X2)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_20])]) ).
cnf(c_0_23,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_21,c_0_22]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET909+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/5.38 % Computer : n020.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Mon Sep 21 05:44:08 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/5.43 Running first-order theorem proving
% 0.15/5.43 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/5.45 % Version: 3.5.1
% 0.15/5.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/5.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/5.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/5.45 % Starting new_bool_3 with 300s (1) cores
% 0.15/5.45 % Starting new_bool_1 with 300s (1) cores
% 0.15/5.45 % Starting sh5l with 300s (1) cores
% 0.15/5.45 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2126109 completed with status 0
% 0.15/5.45 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.15/5.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/5.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/5.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/5.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/5.45 % No SInE strategy applied
% 0.15/5.45 % Search class: FGHSS-FFMS32-SFFFFFNN
% 0.15/5.45 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/5.45 % Starting SubtermCWHack with 136s (1) cores
% 0.15/5.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.15/5.45 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 191s (1) cores
% 0.15/5.45 % Starting new_bool_3 with 191s (1) cores
% 0.15/5.45 % Starting new_bool_1 with 191s (1) cores
% 0.15/5.45 % SubtermCWHack with pid 2126113 completed with status 0
% 0.15/5.45 % Result found by SubtermCWHack
% 0.15/5.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/5.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/5.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/5.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/5.45 % No SInE strategy applied
% 0.15/5.45 % Search class: FGHSS-FFMS32-SFFFFFNN
% 0.15/5.45 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/5.45 % Starting SubtermCWHack with 136s (1) cores
% 0.15/5.45 % Preprocessing time : 0.001 s
% 0.15/5.45
% 0.15/5.45 % Proof found!
% 0.15/5.45 % SZS status Theorem
% 0.15/5.45 % SZS output start CNFRefutation
% See solution above
% 0.15/5.45 % Parsed axioms : 13
% 0.15/5.45 % Removed by relevancy pruning/SinE : 0
% 0.15/5.45 % Initial clauses : 24
% 0.15/5.45 % Removed in clause preprocessing : 0
% 0.15/5.45 % Initial clauses in saturation : 24
% 0.15/5.45 % Processed clauses : 36
% 0.15/5.45 % ...of these trivial : 2
% 0.15/5.45 % ...subsumed : 8
% 0.15/5.45 % ...remaining for further processing : 26
% 0.15/5.45 % Other redundant clauses eliminated : 7
% 0.15/5.45 % Clauses deleted for lack of memory : 0
% 0.15/5.45 % Backward-subsumed : 0
% 0.15/5.45 % Backward-rewritten : 0
% 0.15/5.45 % Generated clauses : 36
% 0.15/5.45 % ...of the previous two non-redundant : 27
% 0.15/5.45 % ...aggressively subsumed : 0
% 0.15/5.45 % Contextual simplify-reflections : 0
% 0.15/5.45 % Paramodulations : 31
% 0.15/5.45 % Factorizations : 0
% 0.15/5.45 % NegExts : 0
% 0.15/5.45 % Equation resolutions : 7
% 0.15/5.45 % Disequality decompositions : 0
% 0.15/5.45 % Total rewrite steps : 9
% 0.15/5.45 % ...of those cached : 4
% 0.15/5.45 % Propositional unsat checks : 0
% 0.15/5.45 % Propositional check models : 0
% 0.15/5.45 % Propositional check unsatisfiable : 0
% 0.15/5.45 % Propositional clauses : 0
% 0.15/5.45 % Propositional clauses after purity: 0
% 0.15/5.45 % Propositional unsat core size : 0
% 0.15/5.45 % Propositional preprocessing time : 0.000
% 0.15/5.45 % Propositional encoding time : 0.000
% 0.15/5.45 % Propositional solver time : 0.000
% 0.15/5.45 % Success case prop preproc time : 0.000
% 0.15/5.45 % Success case prop encoding time : 0.000
% 0.15/5.45 % Success case prop solver time : 0.000
% 0.15/5.45 % Current number of processed clauses : 21
% 0.15/5.45 % Positive orientable unit clauses : 8
% 0.15/5.45 % Positive unorientable unit clauses: 2
% 0.15/5.45 % Negative unit clauses : 5
% 0.15/5.45 % Non-unit-clauses : 6
% 0.15/5.45 % Current number of unprocessed clauses: 14
% 0.15/5.45 % ...number of literals in the above : 38
% 0.15/5.45 % Current number of archived formulas : 0
% 0.15/5.45 % Current number of archived clauses : 0
% 0.15/5.45 % Clause-clause subsumption calls (NU) : 11
% 0.15/5.45 % Rec. Clause-clause subsumption calls : 11
% 0.15/5.45 % Non-unit clause-clause subsumptions : 4
% 0.15/5.45 % Unit Clause-clause subsumption calls : 3
% 0.15/5.45 % Rewrite failures with RHS unbound : 0
% 0.15/5.45 % BW rewrite match attempts : 7
% 0.15/5.45 % BW rewrite match successes : 6
% 0.15/5.45 % Condensation attempts : 0
% 0.15/5.45 % Condensation successes : 0
% 0.15/5.45 % Termbank termtop insertions : 1564
% 0.15/5.45 % Search garbage collected termcells : 415
% 0.15/5.45
% 0.15/5.45 % -------------------------------------------------
% 0.15/5.45 % User time : 0.003 s
% 0.15/5.45 % System time : 0.004 s
% 0.15/5.45 % Total time : 0.007 s
% 0.15/5.45 % Maximum resident set size: 3640 pages
% 0.15/5.45
% 0.15/5.45 % -------------------------------------------------
% 0.15/5.45 % User time : 0.017 s
% 0.15/5.45 % System time : 0.013 s
% 0.15/5.45 % Total time : 0.030 s
% 0.15/5.45 % Maximum resident set size: 4608 pages
% 0.15/5.45 % E exiting
%------------------------------------------------------------------------------